I live in a tall building (20 floors) on a mountain. Because the water pressure from the water company is not enough, there is a water pump at the last floor which is activated each time someone is using fresh water in his apartment.

To me, that's a big waste of energy, and I think that in theory it would be possible to reuse the used water which is going down to pump some fresh water up.

I wonder if such device already exist on the market, and I would like to know how such device would be called. Would there be a problem to operate with such a height difference?

Have you done a calculation or checked the pump's electricity meter (if it has a dedicated one) to see how much power this pump consumes? Assume 100 litres per person per day, and run the numbers: you might be surprised how little energy is needed each day
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EnergyNumbersApr 9 '12 at 16:17

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Even putting aside the economic case, the weight of the systems will contribute to the mass the building has to support, and the energy gains would need to compensate for the additional steel production. It is this feedback between energy, materials, and the rest of our economy that makes it a grand challenge. If energy could be addressed in isolation it would be easy - energy is everywhere!
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Alan RomingerApr 9 '12 at 18:07

Indeed .. it seem that to invest into a better elevator system would be simpler and cheaper than to improve the water system, and would save as much energy .. if not more.
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VincentApr 9 '12 at 18:20

1 Answer
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In theory, yes, this could be done. Pretty much exactly as much gravitational energy is lost by the water coming down as is gained by the water going up, so you could then supply the water while hardly using any energy at all. (Just enough to offset the heat generated by friction in the pipes.)

One way in which it can be done in theory is simply to connect two gear pumps with a solid axel. Water from the down pipe will force the axel to turn, which then drives the up pump. Water can be made to flow by applying just a little bit of extra torque to the axel.

However, in practice I don't think this would be done. I imagine there would be a lot of practical issues involved in passing waste water through a pump - it would at least have to be filtered first - and as EnergyNumbers points out in a comment, the energy needed to pump water up 20 floors is pretty small in comparision to (for example) heating the apartments.